Exemplary embodiments of the invention relate to a method for resolving sub-carrier ambiguities of a total number of tracking channels of a binary offset carrier (BOC) navigation signal comprising a carrier modulated by a code modulation function of a given code rate and further modulated by a sub-carrier modulation function of a given sub-carrier rate. For each channel, the method comprises the steps of generating a first estimate of delay based on the code modulation and generating a second estimate of delay based on the sub-carrier modulation.
In a global navigation satellite system (GNSS), a receiver estimates delays in the navigation signals received from different satellites and uses this information, combined with information on the position of the satellites, to estimate its position. The more accurate the estimation of the delays is, the more accurately the receiver can estimate its position.
In current GNSS systems, navigation signals transmitted by the satellites are modulated using a phase shift keying (PSK) modulation of a code onto a carrier signal having a designated carrier frequency. In next generation GNSS systems, like the Galileo system or an improved American global positioning system (GPS), binary offset carrier (BOC) modulations will be used. Like PSK modulation, BOC modulation involves modulating a code onto a carrier. This code is similar to that used in PSK modulation. However, BOC modulation involves further modulating the signal by a sub-carrier which can be represented by a sub-carrier modulation function having a sub-carrier rate and a sub-chip duration. Consequently, a BOC signal consists of a carrier, modulated with a pseudo random noise (PRN) code, and additionally modulated with a binary sub-carrier.
An auto correlation function of a BOC signal shows multiple peaks, as illustrated in FIG. 1 for a BOC (15, 2.5) signal. As known to the person skilled in the art the first parameter (here: 15) of the BOC signal indicates the subcarrier rate whereas the second parameter (here: 2.5) of the BOC signal indicates the code rate. If a receiver uses early (E) and late (L) replicas for code tracking consisting of a respective PRN code modulated with the sub-carrier, a tracking loop can settle on a sidepeak of the correlation function which introduces a bias in the delay estimate. In case of a BOC (15, 2.5) signal the bias is approximately 9.7 m. In case of a BOC (10, 5) signal, the bias is approximately 14.7 m. Obviously, this bias directly translates into a position error which is highly undesirable.
Different techniques have been proposed to overcome this problem, for example Bump Jumping or Sub-carrier Cancellation (SCC).
U.S. Patent Application Publication No. US 2010/0104046 A1 discloses an approach for BOC signal tracking, which is called Double Estimator technique. The entire disclosure of this Patent Application Publication is herein expressly incorporated by reference. While a tracking loop of a conventional receiver includes two loops for carrier and code tracking, a Double Estimator includes three independent but cooperative loops for the carrier, the sub-carrier and code. A simplified block diagram of a Double Estimator tracking loop is shown in FIG. 2. For clarity, complex signals are used in this representation. An input signal s(t) is mixed with a carrier, generated by a numerically controlled oscillator (NCO) 10. The mixed signal splits up in three branches and is mixed with an early (E), a prompt (P) and a late (L) subcarrier replica, respectively, which are generated by a sub-carrier NCO 12. Next, the signals that were mixed with the early and late subcarrier are mixed with a prompt code replica, the signal that was mixed with the prompt subcarrier is split up in three branches and mixed with an early, a prompt and a late code replica. All code replicas are generated by a code NCO 14. The resulting signals are fed to respective adders connected to discriminators and loop filters 16. The discriminators and loop filters 16 are connected to the NCOs 10, 12, 14.
The Double Estimator of US 2010/0104046 A1 provides two independent delay estimates, one from code tracking, τ, and one from sub-carrier tracking, τ*. The code tracking delay estimate τ is less accurate while the sub-carrier tracking delay estimate τ* is ambiguous with the sub-carrier chip duration Ts. A final delay estimate is calculated by resolving the sub-carrier delay ambiguity using a less accurate code delay estimate as follows:τi+=τi*+TS·Ni.
Ni denotes the sub-carrier ambiguity for a tracking channel i, obtained as follows:
      N    i    =      round    ⁡          (                                    τ            i                    -                      τ            i            *                                    T          S                    )      
However, depending on multipath, dynamics and tracking loop bandwidths, the above rounding operation can fail to resolve the sub-carrier ambiguity correctly which leads again to a bias in the final delay estimate.
Exemplary embodiments of the present invention involve a method providing a more accurate way for resolving sub-carrier ambiguities of tracking channels of a binary offset carrier (BOC) navigation signal.
Exemplary embodiments of the invention involve a method for resolving sub-carrier ambiguities of a total number of tracking channels of a binary offset carrier (BOC) navigation signal comprising a carrier modulated by a code modulation function of a given code rate and further modulated by a sub-carrier modulation function of a given sub-carrier rate, for each channel comprising the steps of generating a first estimate of delay based on the code modulation, and generating a second estimate of delay based on the sub-carrier modulation.
According to exemplary embodiments of the invention, the method involves, for a simultaneously considered subset of at least four tracking channels, determining a set of sub-carrier candidate ambiguities based on the sub-carrier modulation; calculating for each possible combination of sub-carrier ambiguities position and receiver clock error; calculating predicted delays based on each calculated position and receiver clock error; calculating differences between the predicted delays and the delay candidates originating from each specific combination of subcarrier ambiguities; calculating a residual based on the differences; and selecting the set of sub-carrier ambiguities and the corresponding position and receiver clock error which leads to the smallest residual.
Exemplary embodiments of the invention provide a method of jointly resolving the sub-carrier ambiguity for a number of tracking channels and calculating a position and time solution which is more robust with respect to dynamics and multipath than the code-based rounding operation described previously which is applied independently for each channel. Compared to solutions where each tracking channel resolves a sub-carrier ambiguity independent from the other channels, the method provides a solution where the probability for a false sub-carrier ambiguity resolution, and in consequence for a bias position and clock estimate, is smaller.
According to a preferred embodiment the step of calculating a residual comprises squaring and summing the differences between the predicted delays and the delay candidates, providing the residual for a specific combination of sub-carrier ambiguities.
According to a further preferred embodiment ki residuals are calculated with k being the number of ambiguities and i being the number of channels.
It is further preferred when the subset of considered tracking channels comprises a good geometric dilution of precision (GDOP). Especially, for the remaining channels the predicted delays are calculated using the calculated position and receiver clock error. “Remaining channels” are those channels of the total number of tracking channels that are not considered in the subset of tracking channels.
In a further preferred embodiment the sub-carrier ambiguities for the remaining channels are obtained using the calculated predicted delays {circumflex over (τ)}i for the remaining tracking channels. Preferably, the sub-carrier ambiguities for the remaining channels are obtained by:
      N    i    =            round      ⁡              (                                                            τ                ^                            i                        -                          τ              i              *                                            T            S                          )              .  
Alternatively, the sub-carrier ambiguities are obtained using Real-Time Kinematic-technology for carrier phase ambiguity fixing.
In a further preferred embodiment all tracking channels are considered simultaneously.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of one or more preferred embodiments when considered in conjunction with the accompanying drawings.